% The Hurst exponent
%--------------------------------------------------------------------------
% The first 20 lines of code are a small test driver.
% You can delete or comment out this part when you are done validating the
% function to your satisfaction.
%
% Bill Davidson, quellen@yahoo.com
% 13 Nov 2005
function []=hurst_exponent()
disp('testing Hurst calculation');
%--------------------------------------------------------------------------
% This function does dispersional analysis on a data series, then does a
% Matlab polyfit to a log-log plot to estimate the Hurst exponent of the
% series.
%
% This algorithm is far faster than a full-blown implementation of Hurst's
% algorithm. I got the idea from a 2000 PhD dissertation by Hendrik J
% Blok, and I make no guarantees whatsoever about the rigor of this approach
% or the accuracy of results. Use it at your own risk.
%
% Bill Davidson
% 21 Oct 2003
function [hurst] = estimate_hurst_exponent(data0) % data set
npoints=fix(npoints/2);
binsize=binsize*2;
for ipoints=1:npoints % average adjacent points in pairs
data2(ipoints)=(data(2*ipoints)+data((2*ipoints)-1))*0.5;
end
data=data2(1:npoints);
end % while
xvals=xvals(1:index);
yvals=yvals(1:index);
logx=log(xvals);
logy=log(yvals);
p2=polyfit(logx,logy,1);
hurst=p2(1); % Hurst exponent is the slope of the linear fit of log-log plot